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Descriptive properties of spaces of signed measures. (English) Zbl 1069.54024
Descriptive properties of spaces of signed measures on $$X$$ are derived from the respective properties of $$X$$. Similar questions for spaces of non-negative measures were answered by P. Holický and O. Kalenda in [Bull. Pol. Acad. Sci., Math. 47, 37–51 (1999; Zbl 0929.54026)]. The results give answers to questions posed by Holický and Kalenda and they say in particular that: If $$Y$$ is Borel (Suslin from closed, Suslin from Borel, or co-Suslin from Borel sets) in a Tychonoff space $$X$$, then the space $$\mathfrak M_t(Y)$$ of signed Radon measures has the same property in $$\mathfrak M_t(X)\subset (C(\beta X)^*,w^*)$$. However, there are a compact space $$X$$ and an open set $$Y\subset X$$ such that $$\mathfrak M_t(Y)$$ is not co-Suslin from closed sets in $$\mathfrak M_t(X)$$.
##### MSC:
 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 46E27 Spaces of measures
##### Keywords:
signed measures; Borel sets; Suslin sets; Čech-analytic spaces
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